Ivanka Trump has emerged as a key White House player on tax reform, spearheading policies to provide relief to middle-class Americans and staking out common ground with conservative and liberal lawmakers on Capitol Hill.

Over the past months, President Trump’s daughter and senior adviser joined members of the Treasury, the White House National Economic Council and Office of Legislative Affairs for scores of meetings with Congress members, advocacy groups and Washington associations and think tanks.

In the run-up to the introduction last week of the Republican tax reform bill, Ms. Trump joined Treasurer Jovita Carranza at a town-hall-style forum in Bucks County, Pennsylvania, and then teamed with Senate and House members at the Capitol to highlight the urgency of giving working families a bigger child tax credit.

“As a mother herself, Ivanka seemed to speak from the heart, and it was evident she wants to help put the American family first,” said Sen. Tim Scott, a South Carolina Republican on the tax-writing Senate Finance Committee who organized the meeting with Ms. Trump on Capitol Hill.

“She demonstrated that she is committed to using her influential role in a powerful way to be an advocate for working moms and dads,” he said. “Her tenacity on this topic is driven by her motivation to help folks keep more of their hard-earned money.”

At the Pennsylvania event, Ms. Trump argued that a bigger, refundable child tax credit was “critically important to help offer American families much-needed relief and prioritize what’s right for their families.”

“It’s time we recognize as a country that we have to have policies that mirror our values: work and family,” she said of the proposal.

She has made similar pitches at meetings and forums around Washington, including with a bipartisan group of senators at a dinner two weeks ago at her home in the city’s upscale Kalorama neighborhood. Her husband, White House adviser Jared Kushner, and Treasury Secretary Steve Mnuchin also helped make the case for tax reform at the dinner.

The Senate Democrats at the table were some of the party’s most vulnerable incumbents up for re-election next year: Heidi Heitkamp of North Dakota, Joe Manchin III of West Virginia, Claire McCaskill of Missouri and Patrick J. Toomey of Pennsylvania.

Their votes could be crucial to pass tax reform in the narrowly divided Senate.

The bill, rolled out Thursday and undergoing amendments in the House this week, reflects some of Ms. Trump’s priorities.

Under the legislation, the child tax credit would increase from 1,000 to $1,600 per child.

A new credit would provide $300 for dependents older than 18, such as elderly parents needing care or children in college.

However, the House bill fell short of Ms. Trump’s push for doubling the child tax credit. It also kept the maximum refundable portion of the credit at the $1,000 level, adjusted with the chained consumer price index to rise with prices over time until reaching $1,600.

Republican Sens. Mike Lee of Utah and Marco Rubio of Florida shared Ms. Trump’s goal of raising the credit to at least $2,000. They have long advocated a bigger tax credit that is refundable through payroll withholding so working families don’t have to wait for the money.

Mr. Lee and Mr. Rubio called the House bill an important step in the process but saw room for improvement.

“The best way to provide real relief to working families is through a straightforward, significant and permanent expansion of the child tax credit. We wish the House draft had done more on this front — preferably doubling the credit to $2,000 per child and expanding its applicability to payroll taxes. We look forward to working with our colleagues to make sure working families are moved to the front of the line in the Senate bill,” they said in a joint statement.

Ms. Trump has not finished working on tax reform. The president assigned her to the team tasked with mustering support for the legislation while he is traveling in Asia.

She had planned to travel with the presidential delegation, including her husband, White House adviser Jared Kushner, on the 12-day Asia trip.

“Since tax reform is the administration’s top priority, the president asked officials including Secretary Mnuchin, NEC Director [Gary] Cohn and adviser Ivanka Trump to stay in the U.S. and continue to push comprehensive tax reform,” a White House official told The Washington Times.

The effort got underway Sunday with Ms. Trump and Mr. Mnuchin discussing the importance of tax reform at a forum at the Ronald Reagan Presidential Library in Simi Valley, California.

On Monday, Ms. Trump and Mr. Mnuchin were drumming up support for the bill at a business roundtable in Newport Beach, California.

“A central focus of this administration is something I am particularly passionate about — ensuring relief for American working families, which is achieved through a combination of proposals including an expansion of the child tax credit, the preservation of the child and dependent care credit, taxing more income at zero, and lower tax rates for businesses,” Ms. Trump said at the Reagan Library.

“We can’t afford not to support all Americans, especially hardworking American families and their children. They are the future of this great country,” she said. “The tax plan will accomplish this goal.”